Here are some words that rhyme with "shine" according to various online rhyming dictionaries:

• Outshine
• Incline
• Outline
• Sideline
• Skyline
• Bloodline
• Headline
• Moonshine
• Benign
• Grapevine
• Deadline
• Line
• Sign
• Fine
• Mine
• Design
• Wine
• Divine
• Align
• Online

Note that some of these words are perfect rhymes, while others are near rhymes.